Question

The following table shows the Myers-Briggs personality preference and area of study for a random sample of 519 college students. In the table, IN refers to introvert, intuitive; EN refers to extrovert, intuitive; IS refers to introvert, sensing; and ES refers to extrovert, sensing.

Myers-Briggs Preference	Arts & Science	Business	Allied Health	Row Total
IN	66	13	17	96
EN	82	44	28	154
IS	52	37	26	115
ES	72	38	44	154
Column Total	272	132	115	519

Use a chi-square test to determine if Myers-Briggs preference type is independent of area of study at the 0.05 level of significance.

(a) What is the level of significance?

0.05

State the null and alternate hypotheses.

H₀: Myers-Briggs type and area of study are independent.
H₁: Myers-Briggs type and area of study are not independent.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

Are all the expected frequencies greater than 5?

Yes

What sampling distribution will you use?

chi-square

What are the degrees of freedom?


(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

p-value > 0.100

0.050 < p-value < 0.100     

0.025 < p-value < 0.050

0.010 < p-value < 0.025

0.005 < p-value < 0.010

0.005 p-value < 0.010

p-value < 0.005

Answer 1

The statistical software output for this problem is:

Hence,

b) Test statistic = 19.836

Degrees of freedom = 6

c) p-value < 0.005